Analytic continuation of representations and estimates of automorphic forms. (English) Zbl 0934.11023

Bernstein, Joseph; Reznikov, Andre

Ann. Math. (2) 150, No. 1, 329-352 (1999).

The results of the paper under review were announced in [C. R. Acad. Sci., Paris, Sér. I Math. 327, No. 2, 111-116 (1998; Zbl 0915.11030)].
An important result of this work is the proof of the presently best estimate for the Fourier coefficients of Maaß wave forms on arbitrary cofinite subgroups of \(\text{SL}_2(\mathbb{R})\) with cusps (see the preceding review Zbl 0934.11022). The authors’ method of proof makes essential use of representation theory.

Reviewer: J.Elstrodt (Münster)

MSC:

11F30	Fourier coefficients of automorphic forms
11F70	Representation-theoretic methods; automorphic representations over local and global fields
11F72	Spectral theory; trace formulas (e.g., that of Selberg)
58J50	Spectral problems; spectral geometry; scattering theory on manifolds
11M41	Other Dirichlet series and zeta functions
22E30	Analysis on real and complex Lie groups

Keywords:

Fourier coefficients; Maaß wave forms

Citations:

Zbl 0934.11022; Zbl 0915.11030